# Polarization and Fermat's principle

## Homework Statement

a) A beam of light in the air strikes the surface of a smooth piece of plastic having an index of refraction of 1.55 at an angle with the normal of 60 degrees. The incident light has equal component E-field amplitudes parallel and perpendicular to the plane of incidence of 10 V/m. Determine the corresponding reflected field amplitudes.

b) How is the polarization state of the reflected field different from the incident of light? Explain how polarized glasses help suppress glare from the water or glasses surface

## The Attempt at a Solution

I have no idea where to start this!! I know that the angle of the reflected light will be equal to the initial angle of the light, and I could use snell's law to solve for the refracted light, which would be 33.97 degrees if that does anything.

Use the Fresnel formulas ;)

I figured that part out five minutes after i posted this :)

I think I did this right and I got -.0339 for r parallel
and I got -.184 for r perp

Are they both supposed to be negative though? I thought one was supposed to be positive.
Also, I don't know where to go from here. I know that r represents the ratio of the amplitudes, but I wouldn't be able to solve for the original amplitude without the initial amplitudes. All that I have is the intensity.

Any help would be great,

Thanks!

But you have the initial amplitudes they are 10V/m for perp and parallel both ;)

The intensity is the amplitude???

What do you mean? The amplitude of the incident light is 10V/m.
What do you call by intensity?
And the reflection coefficents cannot be negative, you made a mistake in your calculations somewhere ;)

oh I know what happened, I calculated the little r, and the big R is what I'm looking for, so I squared them and got

Rparallel=.00115
Rperp=.1935

So, would I just multiply them by 10 V/m for each one then to get the answer?

The big R gives the reflected intensity. The small r gives the reflected amplitudes. You want the small r as you are looking for the reflected amplitude.

Ok I get that,

But my professor said something about the degree of polarization, which i calculated to be around 98.8% percent or so. What am I supposed to do with that and how does that affect the amplitude?